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On Wednesday 12 January 2005 11:18 am, Steven L. Johnson wrote:
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> Matthew -- I think you'll find the following article really helpful:
> Newman, M. E. J. (2003) "The structure and function of complex networks,"
>      SIAM Review (45) 2, pp. 167-256.
> See section 3.2 in particular (page 17 of the PDF, page 183 of the
> article). Newman talks about two different clustering coefficient
> formulas, which he refers to as C(1) and C(2).
> Newman notes that the Watts & Strogatz definition, C(2), tends to
> weight low-degree nodes more heavily than C(1).
> That leads me to a follow-up question: Can anyone on the list offer
> guidance as to what situations either measure is more appropriate
> for??

Both definitions can be described in words simply enough.  C(1) is "the
probability that two people with a common acquaintance know one another".
(There's some subtleties about that, but that's the basic idea.)  C(2) is
"the probability that two acquaintances of a randomly chosen person know
each other".  Thus the crucial difference is whether you are focusing on
the two people or on their common acquaintance.  One can imagine
experimental designs in which either of these two definitions might be
useful.  Where mathematical calculations are concerned, however, the first
is almost invariably easier to calculate.

Mark Newman

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